This functional equation is known as D'Alembert's functional equation. To solve it, we can make the substitution:
a = x + yb = x - y
which gives us:
x = (a + b)/2y = (a - b)/2
Now, we substitute these values into the given functional equation:
f(a) + f(b) = 2f((a + b)/2)cos((a - b)/2)
This equation is known as D'Alembert's functional equation. It is a well-known functional equation in mathematics.
This functional equation is known as D'Alembert's functional equation. To solve it, we can make the substitution:
a = x + y
b = x - y
which gives us:
x = (a + b)/2
y = (a - b)/2
Now, we substitute these values into the given functional equation:
f(a) + f(b) = 2f((a + b)/2)cos((a - b)/2)
This equation is known as D'Alembert's functional equation. It is a well-known functional equation in mathematics.